Triaxial magnetic anisotropy in the two-dimensional ferromagnetic semiconductor CrSBr

Two-dimensional ferromagnets have recently drawn extensive attention, and here we study the electronic structure and magnetic properties of the bulk and monolayer of CrSBr using first-principles calculations and Monte Carlo simulations. Our results show that bulk CrSBr is a magnetic semiconductor and has the easy magnetization $b$ axis, hard $c$ axis, and intermediate $a$ axis. Thus the experimental triaxial magnetic anisotropy (MA) is well reproduced here, and it is identified to be the joint effects of spin-orbit coupling and magnetic dipole-dipole interaction. We find that bulk CrSBr has a strong ferromagnetic (FM) intralayer coupling but a marginal interlayer one. We also study the CrSBr monolayer in detail and find that the intralayer FM exchange persists and the shape anisotropy has a more pronounced contribution to the MA. Using the parameters of the FM exchange and the triaxial MA, our Monte Carlo simulations show that the CrSBr monolayer has Curie temperature ${T}_{\mathrm{C}}=175$ K. Moreover, we find that a uniaxial tensile (compressive) strain along the $a$ $(b)$ axis would further increase the ${T}_{\mathrm{C}}$.